Experimental and Numerical Researches on the Seismic Behavior of Tubular Reinforced Concrete Columns of Air-Cooling Structures
International Journal of Concrete Structures and Materials
Experimental and Numerical Researches on the Seismic Behavior of Tubular Reinforced Concrete Columns of Air-Cooling Structures
Ning-jun Du 0
Guo-liang Bai 0
Ya-zhou Xu 0
Chao-gang Qin 0
0 School of Civil Engineering, Xi'an University of Architecture and Technology , No. 13, Yanta Road, Xi'an 710055, Shaanxi , China
Tubular reinforced concrete columns of air-cooling condenser structures, which undertake the most weight of air cooling equipment, are the major components to resist lateral forces under earthquake. Once collapsed, huge casualties and economic loss would be caused. Thus, four 1/8 scaled specimens were fabricated and tested through the pseudo-static testing method. Failure modes and crack patterns of the specimens under cyclic loading were observed. Then, finite element models of tubular reinforced concrete columns were established using OpenSees and were verified with the experimental results. Finally, the influence of axial compression ratio and longitudinal reinforcement on energy dissipation capacity and stiffness degradation were studied based on the validated finite element modes. It is confirmed that tubular reinforced concrete columns of air-cooling condenser structure exhibit a moderate ability of energy dissipation, and the nonlinear finite element model could reasonably simulate its seismic behavior. Furthermore, axial compression ratio and longitudinal reinforcement are main factors which affect the seismic behavior of the tubular reinforced concrete columns. The experimental results and simulation method provide an available way to design this kind of large tubular reinforced concrete columns with thin-wall.
tubular reinforced concrete column; seismic performance; pseudo-static test; OpenSees
Compared with the traditional natural draft cooling
process,the direct air-cooling technique can achieve water
conservation nearly 70–80%. So, it has priority to be used in
thermal power plants, especially those built in regions which are
short for water and rich for coal, e.g., North China areas
et al. 2015; Li et al. 2008)
. With the improvement of energy
saving and environment protection requirements, construction
and operation of large capacity air-cooling units in thermal
power plants are imperative to balance the increasing electricity
consumption and water resource shortage.
Generally, the air-cooling structure in a large thermal
power plant mainly consists of tubular reinforced concrete
columns,spatial steel truss platform and A-shaped steel truss.
Tubular reinforced concrete columns have the characteristics
of thin-wall and great sizes, typically which are about 4 m in
diameter, 0.3–0.5 m in thickness and 40 m in height. Spatial
steel truss platform is 4–8 m high. Above the spatial steel
truss platform, there is 10–15 m high A-shaped steel truss on
which most equipment are installed. An air-cooling structure
supports millions of tons of weight of the upper equipment.
Once the columns collapsed under earthquake, huge
casualties and economic loss would be caused.
For common reinforced concrete members, lots of experimental
investigations have been conducted
(Nilson and Arthur 1968;
Bathe and Ramaswamg 1979; Priestly and Benzoni 1996; Priestly
et al. 1996; Lehman et al. 1995; Phan et al. 2007; Hindi 2005;
Hindi et al. 2005; Wang et al. 2014; Afefy and El-Tony 2016;
Jiong 2004; Li and Ren 2009; Elmorsi et al. 1998; Esmaeily and
Shirmohammadi 2014; Shao et al. 2005; Zendaoui et al. 2016; Ren
et al. 2010)
. Previous studies of reinforced concrete members have
demonstrated that slender ratio, material property, axial
compression ratio, reinforcement ratio, detailing art and stirrups played
significant roles in the seismic behavior, especially the hysteretic
performance of reinforced concrete members. While, the seismic
performance, especially hysteretic performance of tubular
reinforced concrete columns with thin-wall and great sizes used in
aircooling condenser structure has not yet been clarified so far.
Additionally, with the fast development of computer
technology, numerical simulation methods play a more and more
important role in the nonlinear analysis of structures. Popular
finite element codes such as Abaqus, Ansys, OpenSees have
been developed to simulate the structural responses of
reinforced concrete members. For circular columns,
et al. (1999)
investigated failure modes of hollow bridge piers
using three-dimensional nonlinear finite element method.
Shirmohammadi and Esmaeily (2015)
proposed an analytical
algorithm and confirmed its accuracy, and it was also used to
perform a parametric study considering the effects of axial
load variation and lateral force/displacement paths on the
flexural strength and energy dissipation capacity of reinforced
Kim et al. (2012)
proposed a framework for
assessment of the seismic performance of hollow reinforced
concrete and prestressed concrete bridge columns.
The primary objective of this study is to investigate the
seismic response and failure modes of tubular reinforced
concrete columns by pseudo-static testing, and develop a simple,
yet reasonably accurate finite element model to predict the
nonlinear cyclic response of this kind of columns. Accuracy of
the FEM model was validated against experimental results.
Furthermore, based on the validated analytical model, a
parametric study was finally carried out to clarify the effect of axial
compression ratio and longitudinal reinforcement on the
ultimate strength, ductility and energy dissipation capacity.
2. Experimental Program
The prototype air-cooling structure was located in Jinjie
thermal power plant, whose full-scale tubular reinforced
concrete columns are 24.6 m high with outer diameter of
4 m and thickness of 0.4 m, as shown in Fig. 1. As
wellknown, axial compression ratio and reinforcement ratio play
an important role on the seismic performance of concrete
structures. In consideration of the characteristics of thin wall
and large size for the tubular reinforced concrete columns,
reinforcement ratio, thickness and axial force were chosen as
the test variables. The axial force exerted on the specimen
was determined based on the axial compression ratio of the
prototype air-cooling structure columns under different
combined load cases. Confined to the laboratory condition
and consideration of economy, four 1/8 scaled specimens
were fabricated and tested through pseudo-static testing in
present works. According to the similarity law,four scaled
specimens are 3.07 m high with outer diameter of 0.5 m.
2.1 Details of Specimens
2.1.1 Determination of the Axial Compression
The axial force exerted on the specimen was determined
based on the axial compression ratio of the prototype
aircooling structure columns under different combined load
cases (Table 1).
In Table 1, DL is dead load, LL is live load, S is snow
load, W is wind load and EQ is earthquake action. X and Y
are the directions of the earthquake. According to the
Table 1, 0.09, 0.15, 0.20 was taken for the test.
2.1.2 Determination of Specimen Section
The cross section of the prototype column is
4000 9 400 mm while the cross section of the scaled
column is 500 9 50 mm according to the 1/8 scaled ratio. In
order to investigate whether the change of wall thickness
will influence the seismic performance of columns, the cross
sections of 500 9 70 mm and 500 9 100 mm were
designed. 15, 16, 22, 20 longitudinal steel bars with the
diameter of 10 mm were used in the Tube1–Tube4,
respectively. The circular stirrup was 8 mm in diameter and
arranged with the spacing of 200 mm except for the top and
bottom 500 mm of the columns, in which the spacing is
100 mm. Experimental yielding strength values of steel
reinforcement and circular stirrup were 461.7 and
2.1.3 Determination of the Axial Force
The axial force N was calculated by the following
where n denotes the axial compression ratio, fcs is measured
value of concrete compression strength and A is the area of
cross section. Take Tube1 for example, N ¼ nfcsA ¼
0:09 28:88 70650 ¼ 180 kN.The detailed dimensions
and material properties are listed in Table 2, where fcuk and
Diameter (mm) Thickness (mm) Axial Force (kN)
fck denote the cubic compression strength of concrete and
prism compression strength of concrete, respectively.
The spacing of the specimens is shown in Fig. 2. The
detailed dimensions and material properties are listed in
Table 2, where fcuk and fck denote the cubic compression
strength of concrete and prism compression strength of
2.2 Test Setup and Instrumentation Layout
Four specimens were tested by an electro-hydraulic servo
system of MTS. The testing setup is manifested in Fig. 3.
2.3 Loading System
During the testing process, the vertical axial force was
firstly applied on the top of the specimens with specified
values and kept constant. The cyclic lateral displacement
was then exerted to simulate seismic action through
displacement control method. The specific loading system is as
2.3.1 Axial Compression Load
(1) A 3-mm initial cyclic lateral displacement was exerted
through the MTS actuator at first. Then, the value of
the target displacement increased with increment of
1 mm each cyclic until visible cracks were observed on
the specimens during the loading system.
Target displacement (mm)
Loading rate (mm/s)
(2) The displacement increment value and the cycle
number then increased to 2 mm and 2 times during
the loading process until the specimen yielded. The
yield point of the specimen was determined
according to the load–displacement curve.1000kN, ±
Target displacement (mm)
Target displacement (mm)
Cycle number Loading rate (mm/s) 1 2
(3) The target displacement and the cycle number were
next adjusted according to the yield displacement. The
displacement increment was multiples of the yield
displacement. When the bearing capacity of a specimen
dropped to 85% of its ultimate load, the loading
process was terminated.
The detailed loading procedures of each specimen are
listed in Table 3, 4, 5 and 6.
3. Experimental Results And Specimen
3.1 Failure Mode
The experimental crack distributions of four specimens are
shown in Fig. 4. For Tube 1, when the top lateral
displacement reached 4 mm, the visible bending cracks occurred
50 mm away from the bottom of the column. Then, the
existing cracks continued to widen and extend while new
cracks successively appeared. When the lateral displacement
at the top of Tube 1 was 115 mm, large pieces of cover
concrete at the bottom of the column spalled, longitudinal
reinforcement buckled and bearing capacity dropped sharply,
which indicated the specimen was severely damaged. The
failure phenomena of Tube2–Tube4 are not repeated here
due to the similarity to Tube 1.
As shown in Fig. 4, it was observed that the scope of
cracks appearance can reach 3/4 of the column height. The
crack distribution of the tubular columns demonstrates that
in comparison to the conventional circular columns there is
need for more zones with dense stirrups to improve the
ductility of the columns.
3.2 Lateral Load versus Displacement Relationship
Experimental hysteretic curves of four specimens are
shown in Fig. 5. It can be found that the tubular reinforced
concrete columns show typically hysteretic features of
reinforced concrete columns. It means, the
load–displacement curves are nearly straight before yielding. With the
development of cracks, the load–displacement curves show
the feature of degradations of strength and stiffness and
‘‘pinching’’ effect. As shown in Fig. 5c, Tube 3 exhibits
poorer ductility due to its higher axial compression ratio
compared with other columns.
The skeleton curves of four specimens are shown in
Fig. 6. The characteristic points, including crack load and
displacement, yielding displacement and load, ultimate load
and ultimate displacement, are listed in Table 7. The
cracking loads were observed and recorded when initial
cracks occurred while the corresponding displacements were
named crack displacement. The yielding points could be
obtained by using the modified general yield bending
moment method. The peak value of a skeleton curve was
defined as ultimate load, while the displacement value
corresponding to 0.85 times of the ultimate load on the skeleton
curve was specified as ultimate displacement.
3.3 Calculation of Normal Section Strength
According to the Code for design of concrete structures of
China, for ring-shaped section eccentric compression
members (Fig. 7) with longitudinal steel reinforcements
uniformly provided along the periphery, the normal section
compressive load-bearing capacity may conform to the
aa1fcA þ ða
a1fcAðr1 þ r2Þ
sin pa þ fyAsrs ðsin pa þ sin patÞ
The coefficient and eccentricity in above equations shall be
calculated according to the following equations:
at ¼ 1
ei ¼ e0 þ ea
where A area of ring-shaped section; As area of section for all
longitudinal ordinary steel reinforcementsm; r1, r2 interior,
exterior radius of ring-shaped section respectively; rs radius
of circumference, where the centroid of longitudinal
ordinary steel reinforcements is situated; e0 eccentricity of axial
compression force to centroid of section; ea additional
eccentricity; a value for ratio of sectional area of concrete in
compression zone to full sectional area of concrete; at value
for ratio of sectional area of longitudinal tension steel
reinforcements to area of all longitudinal steel reinforcements.
The calculation method specified in Code for design of
concrete structures of China is suitable for the conventional
circular columns with large ratio of thickness to diameter.
Tubular reinforced concrete columns have the characteristics
of small ratio of thickness to diameter due to the thin-wall
and great sizes. It is necessary to verify the applicability of
the method in the code. The ultimate bending moment
obtained through the method in the code and the
pseudostatic test are shown in Table 8.
The comparison in Table 8 shows that it is conservative to
calculate the normal section bearing capacity through the
method proposed by the Code for design of concrete
structures of China.
4. Numerical Simulation
OpenSees is an object-oriented framework for building
models of structural and geotechnical systems to perform
nonlinear analysis. OpenSees supports a wide range of
simulation applications in earthquake engineering and its
good nonlinear numerical simulation precision has been
4.1 Finite Element Model
Here, the tubular reinforced concrete columns were
simulated with the fiber model. The finite element models are
fixed at the bottom ends, while free at the top ends, see in
Fig. 8. The fiber section command was used to construct a
uniaxial fiber object and add it to the section. The cross
section of specimens could be divided into several small
patches. According to the plane section assumption,
OpenSees automatically calculates the strain of each fiber and
ensure forces of the cross section keeping balance through
iterative treatment. To model the whole columns, a nonlinear
beam-column element based on the non-iterative force
formulation was employed while considering the spread of
plasticity along the element.
4.2 Constitutive Laws of Steel and Concrete
As well-known, it is crucial to select a reasonable concrete
and steel material models in the nonlinear finite element
simulation. Three concrete stress–strain material models are
available in the OpenSees code, i.e., Concrete0 l,
Concrete02 and Concrete03. Concrete02, a linear tension
softening material model in which the compression skeleton
curve is specified by the Kent-Park stress–strain relationship
(Kent and Park 1971)
, was used to construct a uniaxial
concrete material with a linear tension softening branch.
Since the restraint effect of stirrups on concrete was so
small that it could be ignored and concrete was treated as an
unconfined material according to the researches of Mander
et al. (1998) and
Scott et al. (1982)
Figure 9 displays the monotone and hysteretic stress–
strain rules of Concrete02.The uniaxial compressive stress–
strain relationship of Concrete02 is regulated as
f ¼ Kfco 2
f ¼ Kfco½1
where f, e, fco, ecc are stress, strain, axial compressive
strength and peak strain, respectively.The slope of the strain
softening part can be written as
145fco 1000 þ 0:75qs
where h0 and Sh are the width of core concrete and stirrup
spacing. K denotes the coefficient of concrete strength
increased by the cyclic-hoop effect.
K ¼ 1 þ fco
In Eq. (10), qs and fyh denote the volumetric percentage of
stirrups and corresponding yielding strength. When K equals
to one, Eqs. (6)–(11) are considered as the stress–strain
relationship of unconstrained concrete.In addition, the
uniaxial tension stress–strain relationship of Concrete02 is
rc ¼ Ecec ðec
rc ¼ ft 1
rc ¼ 0 ðecr
e0t ¼ Ec
where Ec and ft denote the initial elastic modulus and axial
tensile strength of concrete. l is the tension hardening
There are two steel stress–strain material models in
OpenSees: Steel0l and Steel02. Here, Steel02 material
command is implemented as the constitutive law of steel. It
was originally suggested by
Menegotto and Pinto (1973)
Then, this model was modified and the influence of strain
hardening was taken into account. Since the stress–strain
relationship of Steel02 is expressed in an explicit form, so it
has high computational efficiency. Lots of simulation results
have demonstrated its good consistency. Figure 10 shows
the monotonic and hysteretic stress–strain curves of Steel02.
The Menegotto-Pinto stress–strain relationship can be
r ¼ b e þ ð1 bÞ e
ð1 þ e RÞ1=R
Equations (16)–(19) represents a curved transition from one
straight line asymptote (E0) to another (E1). b is a parameter
which reflects the strain-hardening ratio of steel. Figure 11
demonstrates the definition of points such as (r0, e0) and (rr,
er). (r0, e0) denotes stress, strain at the point where the initial
tangent and the asymptotes of the curve meet. (r0, e0) denotes
stress, strain at the last reversal point. Parameter R can reflect
the Bauschinger effect of reinforcement and have an influence
on the shape of transition curves. R can be calculated through
equation RðnÞ ¼ R0 ða1 nÞ=ða2 þ nÞ, where R0 is the
initial value of parameters R for the first loading. Values of a1, a2,
R0, can be obtained by experimental results.
In order to take the isotropic hardening effect into account
and improve the Menegotto-Pinto model,
Filippou et al.
proposed that the linearized yielding asymptote should
be adopted. The translation value can be then written as
where es max, ey, fy are the maximum absolute value of
reverse strain, yielding strain and yielding stress of steel.
Parameters, a3, and a4, can be identified in terms of
R0 is the parameter which determines the transition from
elastic to plastic braches and the recommended values are
10–20 according to the OpenSees user’s manual and
(Mazzoni and McKennna 2003; Mazzoni
et al. 2003)
. a1 is the isotropic hardening parameter which is
related to the increase of compression yield envelope after a
plastic strain of a2*fy/E0. a2 and a4 are the isotropic
hardening parameters. a3 is the isotropic hardening parameter
which is related to the increase of tension yield envelope
after a plastic strain of a4*fy/E0. In order to determine these
parameters in the absence of detailed testing results of the
materials, it is necessary to identify the values of the
parameters in a reasonable range during the simulation
process, so that the simulation results are in good accordance
with the experimental results of the columns. Then, the
verified FEM models can be employed to study the influence
of the axial force, and so on.
For finite element simulations, the axial force was firstly
applied and the displacement on the top node was then
exerted to simulate lateral loading. Finally, Newton
algorithm and norm displacement increment method were
adopted to find numerical solutions.
4.3 Model Validation
Figure 12 shows the comparison of the experimental and
numerical hysteretic curves. It can be found that the
OpenSees models can capture the main hysteretic features of
tubular reinforced concrete columns, and the simulation
results match well with the experimental ones as a whole.
Taking Tube 1 for instance, the experimental ultimate load
and ultimate displacement are 59.1kN and 23.3 mm, the
numerical results are 58.4kN and 26.0 mm.
However, the predicted hysteretic curves by OpenSees are
much more plump and the pinching effect is not obvious as
the experimental one. Adopting plane section assumption
and no consideration in bond-slip between concrete and steel
should be the main reason. In fact, due to the uncertainty of
the experiment and deficiency of numerical models, it is
b ¼ E0
often difficult to accurately simulate the declining branches
and pinching effect of experimental results.
5. Parametric Studies
As well-known, ductility and energy dissipation capacity
are mainly influenced by parameters such as ratio of axial
compression and longitudinal reinforcement. Owing to the
limited number of specimens, numerical simulation was then
performed to investigate the influence of parameters based
on the validated finite element models.
5.1 Influence of Axial Compression Ratio
In order to investigate the influence of axial compression
ratio on the bearing capacity, energy dissipation capacity and
stiffness of columns, the magnitude of axial load was
adjusted. New models were designed on the basis of Tube2
(3.07 m high, diameter 500 mm, wall thickness 100 mm)
and values of the axial compression ratio were 0.14, 0.20,
0.25, 0.30, 0.35, 0.40, respectively. The horizontal
Fig. 13 Park method.
displacement on the top of the column was in accordance
with the sequence of 0.2Dy, 0.4Dy 0.6Dy, 0.8Dy, Dy, 1.5Dy,
2Dy, 3Dy, 4Dy, 5Dy, 6Dy, 7Dy, 8Dy. Here, Dy is the equivalent
yield displacement which can be calculated by the Park
method (Fig. 13).
5.1.1 Hysteretic Loops and Skeleton Curves
The simulation results of the hysteretic loops and skeleton
curves are shown in Figs. 14 and 15.
It is obvious that with the increase of axial pressure ratio,
the corresponding maximum load also increases. However,
as the axial compression ratio is exceedingly large, the
ultimate load increases slowly.
It also can be found that the smaller axial compression ratio
is, the less the skeleton curve declines. Therefore, taking the
importance of tubular reinforced concrete columns into
Fig. 15 Skeleton curves with different axial compression ratio
Fig. 16 Parameters meanings of Eqs. (21) and (22).
account, it is indispensable to restrict the maximum value of
the axial compression ratio to ensure the seismic performance.
5.1.2 Energy Dissipation Capacity
Energy dissipation capacity of structures or components is
often measured by the energy dissipation coefficient E and
equivalent viscous damping coefficient he. These two
coefficients are defined as
E ¼ SðOBEþODFÞ
Meanings of the parameters in above formulas are shown in
Based on the simulation results of cyclic loading, energy
dissipation coefficient E and equivalent viscous damping
coefficient he with different axial compression ratio for
Tube2 during yielding stage and limit stage can be calculated
through Eqs. (21) and (22), see in Table 9.
From Table 9, it is easy to find that the equivalent viscous
damping coefficient he and energy dissipation coefficient
E in the limit stage are bigger than the yielding stage. As
expected, with the increase of axial compression ratio, the
equivalent viscous damping coefficient he, energy
dissipation coefficient E and energy dissipation capacity of the
columns decreases gradually. This is mainly because that as
a large eccentric compression member, the height of
compression zone for tubular reinforced columns is relatively
small which is in favor of energy dissipation capacity and
ductility. If the axial compression ratio increases, the height
Fig. 18 Hysteretic loops with different longitudinal reinforcement ratio for Tube2 a q = 1.00% b q = 1.25% c q = 1.56%
d q = 1.87%.
Fig. 19 Skeleton curves with different longitudinal
ment ratios for Tube2.
of relative compression zone will increase as well which
would weaken the ductility and energy dissipation
performance of the columns. When the axial compression ratio is
too large, the tubular reinforced columns would become
members with large compression zones, which deteriorates
the energy dissipation capacity and ductility.
Stiffness degradation can reflect the capacity of resistance
to lateral collapsing, which can be measured by secant
stiffness. Secant stiffness is the ratio of peak load at each
loading level and the associated displacements in positive
and negative direction. It is calculated by the formula below
where Fi and Xi and are the peak load and peak
displacement.The stiffness degradation of the specimens with
different axial compression ratio for Tube2 is illuminated in
One can find that values of the secant stiffness for the
tubes with higher axial compression ratio are larger than the
others. With the development of plastic deformation, the
tendency of stiffness degradation gradually becomes
jþFij þ j Fij
jþXij þ j Xij
moderate. Figure 17 also shows that the tubes with different
axial compression ratio share the same pattern of stiffness
5.2 Influence of Longitudinal Reinforcement
On the basis of Tube 2 and Tube 4, finite element models
with different longitudinal reinforcement were established to
study its influence on the bearing capacity, energy
dissipation capacity and stiffness degradation. The longitudinal
reinforcement ratios of these 4 models are 1.00, 1.25, 1.56,
1.87, respectively. The loading procedure is the same as
5.2.1 Hysteretic Loops and Skeleton Curves
The simulation results of the hysteretic loops and skeleton
curves with different longitudinal reinforcement ratios are
shown in Figs. 18, 19. The simulated results indicate that the
ultimate load of tubular columns enhances obviously with
the increase of longitudinal reinforcement ratio, which is
also beneficial to seismic ductility.
5.2.2 Energy Dissipation Capacity
Table 10 shows the energy dissipation capacity of the
tubes under different longitudinal reinforcement ratios.
Studies of energy dissipation coefficient E and equivalent
viscous damping coefficient he suggest that E and he in
yielding stage and limit stage become larger with the
increase of longitudinal reinforcement ratio. This
demonstrates again that longitudinal reinforcement ratio is in
favor of improving energy dissipation capacity of the tubular
The stiffness degradation of the numerical specimens with
different longitudinal reinforcement ratios for Tube2 is
illuminated in Fig. 20. It can be seen that, within a certain
range, increasing longitudinal reinforcement ratio could
relieve stiffness degradation and improve the ductility of
In this study, a pseudo-static test and experimental results
for four 1/8 scaled tubular reinforced concrete columns of
air-cooling condenser structures are reported. Seismic
behaviors, hysteretic properties and failure modes were
evaluated based on experimental results. Then, finite element
models using OpenSees were established to simulate their
hysteretic loops. The constitutive laws in OpenSees, Steel02
and Concrete02, were chosen to model the behaviors of steel
and concrete subjected cyclic loading. At last, numerical
specimens were established to investigate the influence of
axial compression ratio and longitudinal reinforcement ratio
on bearing capacity of the columns.
From the results of the experimental and analytical studies,
the following conclusions were reached:
(1) Tubular reinforced concrete columns of air-cooling
condenser structures exhibit a moderate ability of
(2) The predicted results obtained by the OpenSees finite
element can reasonably capture the main features of the
tubular reinforced concrete columns. Nevertheless, it is
hard to accurately simulate the severe damage stage of
the experimental results. Further researches are still
needed to improve the accuracy and convergence for
(3) With the increase of axial pressure ratio, the
corresponding maximum load also increases. But after the
axial compression ratio reaches a certain value, the
skeleton curves drop much more steeply and exhibits
poor ductility. Besides, longitudinal reinforcement is
indeed in favor of improving the seismic performance
of the reinforced concrete tubular columns.
It is conservative to calculate the normal section
bearing capacity through the method proposed by the
Code for design of Concrete Structures of China.
Besides, the crack distribution of the tubular columns
demonstrates that in comparison to the conventional
circular columns there is need for more zones with
dense stirrups to improve the ductility of the
The support of the Natural Science Foundation of China
(Grant No. 51478381,51578444) and Ministry of Education
Plan for Yangtze River Scholar and Innovation Team
Development (No. IRT13089) is acknowledged.
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